Microtubules on Curved Surfaces

This is a work in progress talk by a local grad student.

The self-organization of ordered cortical microtubule arrays plays an important role in the development of plant cells. This is observed to emerge from a combination various factors such as microtubule-microtubule interactions, nucleation, and localization of microtubule-associated proteins. Distilling this process into the interaction of one-dimensional bodies on the two-dimensional cortex, quantitative models have been proposed to emulate array formation. These have assisted in understanding the importance of each aspect in addition to identifying potential avenues of experimentation. Until recently, the direct mechanical influence of cell geometry on the constrained microtubule trajectories have been largely ignored in computational models. Modelling microtubules as thin elastic rods constrained on a surface, it has been found that microtubule shapes resulting from curvature minimization may differ significantly from the previously assumed geodesic paths. Restricting to cylinders, we formulate a model incorporating the mechanics of curvature-induced deflection and implement this in an event-driven simulation. Based on some preliminary simulations using our model, we find that the curvature mechanics provides a strong influence for directional alignment – potentially challenging previously drawn conclusions. This simulation provides the opportunity for further exploration into mechanical influences on array formation and their regulation through microtubule-associated proteins.